I also have this issue whilst the Run - Console Type is set to Internal Terminal.
Windows 7 64-bit.
CYGWIN_NT-6.1 Daveoh-PC 1.7.23(0.268/5/3) 2013-08-09 10:05 x86_64 Cygwin
I have another issue whilst console type is set to Standard Output, but I presume that should go in a separate bug report.

OK.. Things appears to be slightly more complicated...
The fix that I can propose for now will allow to proceed with the execution when bitness of all components (jdk, application to run, cygwin) matches.
The bottom line is that one should start netbeans64.exe (and have 64-bit java) with cygwin64 and netbeans.exe (and have 32-bit java) with cygwin32.
At the moment cygwin64 still have several problems that makes it impossible to reliably use current approach for execution (mostly unbuffer.dll bitness mismatch. it is used for starting processes in an 'Output Window' and is a hack to deal with buffered output).
It is too late for the current release to try to overcome these problems and, seems there is no real need in this as cygwin may fix their loose ends at some point.
Changesets: http://hg.netbeans.org/cnd-main/rev/2b8a5a621d68

Some additional info (just for the record) that reflects the current state.
A bitness of jdk/netbeans is important. Possible options are:
1) 32-bit NB and only 32-bit cygwin is installed
2) 32-bit NB and only 64-bit cygwin is installed
3) 32-bit NB and both 32/64-bit cygwin are installed
4) 64-bit NB and only 32-cygwin is installed
5) 64-bit NB and only 64-cygwin is installed
6) 64-bit NB and both 32/64-bit cygwin are installed
Cases 1) and 5) are 'ideal' - in this case everything should work and it is *highly recommended* that bitness of NB/cygwin match. This means that if one tries to use cygwin64 (s)he *should* install 64-bit java and run 64-bit version of NetBeans (netbeans64.exe).
Case 2) is almost nonfunctional. It requires cygwin64/bin to be in %Path%; compilation will work, but run is possible in 'External Terminal' only.
Case 3) NB will detect 32-bit cygwin and will use it by default. IF user tries to add cygwin64 as a toolchain and compile his code in 64-mode, run in 'Output Window' will not work. 32-bit toolchain is OK in this case
Case 4) is almost nonfunctional. It requires cygwin/bin to be in %Path%; compilation will work, but run is possible in 'External Terminal' only.
Case 6) 64-bit compilation/run will work, 32-bit run will fail.